Solving this minimization problem over \(\alpha _j\)  [1]}, [2]}, we obtain
\(p^* := \min _{\mathbf {W}_{1j}, \mathbf {W}_{2j}} \sum _{i=1}^n \mathcal {L}(\sum _{j=1}^m g({\mathbf {X}}_i; \mathbf {W}_{1j}) \mathbf {W}_{2j}, \mathbf {Y}_i) + \beta \sum _{j=1}^m \Vert \mathbf {W}_{1j}\Vert _F \Vert \mathbf {W}_{2j}\Vert _F.\) 
